Lucretius is best known for his long poem On the Nature of Things (De Rerum Natura), which is principally a defense of the ideas of Epicurus, especially the idea of free will, based on Epicurus's introduction of some chance into the universe.

Lucretius is our most direct source for Epicurus' ideas. To break the causal chain of determinism implicit in Democritus' cosmology of atoms in a void, Epicurus postulated an occasional "swerve" of the atoms from their determined paths. We now know that atoms are "swerving" (with unpredictable motions) whenever they come near other atoms. So Epicurus' assumption does indeed break the causal chain of determinism.

Determinism and indeterminism then become the two horns of a dilemma in the standard argument against free will. If we are determined, we are not free, if we are random, we do not control our will.

But Epicurus surely was not thinking our choices and decisions are random, since he hoped to ensure moral responsibility. He explicitly cited necessity (ἀνάγκη) and chance (τύχη) as two kinds of causes, but (following Aristotle) he maintained that our autonomous agency is a third kind (a tertium quid) of cause that is "up to us" (παρ’ ῆμᾶς), obviously meaning it is neither of the first two. But the Stoics (notably Chrysippus, and even the Academic Cicero) destroyed Epicurus' reputation, and it has not recovered to this day.

Lucretius describes the need for some indeterminism, and more strongly than Epicurus, locates the swerving first-beginnings in the mind:

Again, if all motion is always one long chain, and new motion arises out of the old in order invariable, and if the first-beginnings do not make by swerving a beginning of motion such as to break the decrees of fate, that cause may not follow cause from infinity, whence comes this free will in living creatures all over the earth, whence I say is this will wrested from the fates by which we proceed whither pleasure leads each, swerving also our motions not at fixed times and fixed places, but just where our mind has taken us? For undoubtedly it is his own will in each that begins these things, and from the will movements go rippling through the limbs.

What keeps the mind itself from having necessity within it in all actions, and from being as it were mastered and forced to endure and to suffer, is the minute swerving of the first-beginnings at no fixed place and at no fixed time.

Lucretius says clearly that the atomic swerve (clinamen, declinando) breaks the bonds of fate (fati foedera rumpat). He then says that "we swerve" (declinamus) our own motions - just where our mind takes us. One can clearly read this as motions that are "up to us," not that our actions are random. But it is easy to see how (Stoic and Academic) critics could charge him with making the mind and actions depend on chance.

The "first beginning" (primordia motus principium) seems to be a reference to Aristotle's first motion (ἀρχή) and a kind of causa sui that would start additional new causal chains under the control of the mind ("just where our mind has taken us").

The Latin original (lines 256-7) actually says - "whence comes this freedom" (libera), not "will" (cf. voluntas in line 257). Most translators, influenced by the centuries old free will debate, translate libera as "free will."

But Lucretius himself clearly distinguishes the "free" (libera) from the "will" (voluntas). Seventeen centuries later, John Locke said that to think of the will itself as free (in the sense of uncaused and random) is a major source of philosophical confusion.

Moreover, Lucretius describes a temporal sequence of events in the mind, first "free" then "will." Lucretius describes first (primum) the images or "idols" (simulacra, ἐιδόλα) that enter the mind randomly (accidere).
Compare William James's view that ideas just "pop into our heads."

Only then (inde, next) comes the willed action (voluntas) that moves the body.

"In the first place, images of walking (primum simulacra meandi, line 881) happen (accidere, accidently) in our mind and give an impulse to our mind ...Next after this comes the will (inde voluntas fit, line 883)."

In De Rerum Natura, Book 4, lines 877-906, he says (Rouse translation):

877 Next I will say how it comes about that we can carry onwards our steps when we please, how it has been given to us to move our limbs in different ways, what has caused the habit of pushing onwards this great bodily weight: do you attend to my sayings.

881 I say that in the first place images of movement come in contact with our mind, and strike the mind, as I said before.

After this comes will; for no one ever begins anything until the intelligence has first foreseen what it wills to do. (What it foresees, the image of that thing is present in the mind.)

Therefore when the mind so bestirs itself that it wishes to go and to step forwards, at once it strikes all the mass of spirit that is distributed abroad through limbs and frame in all the body. And this is easy to do, since the spirit is held in close combination with it. The spirit in its turn strikes the body, and so the whole mass is gradually pushed on and moves...

898 Again, there is no need to be surprised that elements so small can sway so large a body and turn about our whole weight. For indeed the wind, which is thin and has a fine substance, drives and pushes a great ship with mighty momentum, and one hand rules it however fast it may go, and one rudder steers it in any direction; and a machine by its blocks and treadwheels moves many bodies of great weight and uplifts them with small effort.

What Lucretius said about the "idols" - images that strike the mind, shows not only that they are many, spontaneous, and random (accidental), but they can combine to form purely imaginary images, like the centaur.

In De Rerum Natura, Book 4, lines 722-48, he says:

722 Now listen, and hear what things stir the mind, and learn in a few words whence those things come into the mind that there do come.

724 In the first place I tell you that many images of things are moving about in many ways and in all directions, very thin, which easily unite in the air when they meet, being like spider's web or leaf of gold. In truth these are much more thin in texture than those which take the eyes and assail the vision, since these penetrate through the interstices of the body, and awake the thin substance of the mind within, and assail the sense.

732 Thus it is we see Centaurs, and the frames of Scyllas,a and faces of dogs like Cerberus, and images of those for whom death is past, whose bones rest in earth's embrace, since images of all kinds are being carried about everywhere, some that arise spontaneously in the air itself, some that are thrown off from all sorts of things, others that are made of a combination of these shapes. For certainly no image of a Centaur comes from one living, since there never was a living thing of this nature; but when the images of man and horse meet by accident, they easily adhere at once, as I said before, on account of their fine nature and thin texture. All other things of this class are made in the same way. And since these are carried about with velocity because of their extreme lightness, as I explained before, any given one of these fine images easily bestirs our mind by a single impression; for the mind is itself thin and wonderfully easy to move.

On Possible Worlds

526 for which of these causes holds in our world it
is difficult to say for certain ; but what may be done
and is done through the whole universe in the various
worlds made in various ways, that is what I teach,
proceeding to set forth several causes which may
account for the movements of the stars throughout
the whole universe; one of which, however, must
be that which gives force to the movement of the
signs in our world also ; but which may be the true
one,